The Woking-based team displayed good pace at the German GP and that continued on Friday morning as Hamilton and fellow Briton Jenson Button topped the timesheets.
Hamilton, who went top after just 34 minutes - soon after arriving on track for a first serious run - was never threatened. He was ultimately a tenth of a second quicker than his team-mate, with his benchmark time a minute 22.821 seconds.
In positions six to 10 were Rosberg's German compatriot and team-mate Michael Schumacher, Felipe Massa in the sister Ferrari, Lotus' Kimi Raikkonen, Williams test driver Valtteri Bottas and Sauber's Sergio Perez.
The consistent Alonso holds a 34-point lead in the standings from Mark Webber, with world champion Sebastian Vettel in the sister RB8 10 points further back. Raikkonen is fourth for Lotus, with Hamilton and Button down in fifth and seventh, separated by Rosberg.
But there are signs of a McLaren fightback ahead of the annual summer break, with the Red Bulls of Webber and Vettel only 13th and 15th in the opening session in Hungary respectively - almost two seconds slower than Hamilton.
With medium tyres in evidence for much of the running, it could be that the gap will close as the weekend progresses.
However Webber needed extensive work on the front wing of his car two-thirds of the way through the session as Red Bull sought to improve their aerodynamics, while Ferrari and McLaren seemed happier with their initial set-ups.